Conic sheaves on subanalytic sites and Laplace transform

Abstract

In this paper we give a construction of conic sheaves on a subanalytic site and we extend the Fourier-Sato transform to this framework. Let E be a n dimensional complex vector space and let E^* be its dual. As an application we construct the conic sheaves $\OO^t_{E_{\RP}}$ and $\OO^w_{E_{\RP}}$ of tempered and Whitney holomorphic functions respectively and we give a sheaf theoretical interpretation of the Laplace isomorphisms of Kashiwara and Schapira which give the isomorphisms in the derived category $\OO^{t\land}_{E_{\RP}}[n] \simeq \OO^t_{E^*_{\RP}}$ and $\OO^{w\land}_{E_{\RP}}[n] \simeq \OO^w_{E^*_{\RP}}$.